Precise constraints on the dark matter content of Milky Way dwarf galaxies for gamma-ray experiments

TL;DR

This work addresses how precisely the dark matter content of Milky Way dwarf spheroidal galaxies can be constrained for gamma-ray experiments. By fitting velocity-dispersion data with smooth NFW-like halos and applying CDM priors, the authors derive robust constraints on the density–scale parameters ρ_s and r_s, and thus on the annihilation luminosity L that governs the gamma-ray flux. They find Ursa Minor and Draco as the most promising targets in the smooth-halo case, and show that substructure can boost the flux by up to ~100, while the predicted fluxes across the six dSphs remain tightly correlated, with ratios known within about an order of magnitude and CDM priors reducing uncertainties to roughly 3–6. These results provide concrete guidance for gamma-ray searches and suggest that stacking signals from multiple dSphs could enhance detectability while offering robust, model-informed flux predictions.

Abstract

We examine the prospects for detecting gamma-rays from dark matter annihilation in the six most promising dwarf spheroidal (dSph) satellite galaxies of the Milky Way. We use recently-measured velocity dispersion profiles to provide a systematic investigation of the dark matter mass distribution of each galaxy, and show that the uncertainty in the gamma-ray flux from mass modeling is less than a factor of ~ 5 for each dSph if we assume a smooth NFW profile. We show that Ursa Minor and Draco are the most promising dSphs for gamma-ray detection with GLAST and other planned observatories. For each dSph, we investigate the flux enhancement resulting from halo substructure, and show that the enhancement factor relative to a smooth halo flux cannot be greater than about 100. This enhancement depends very weakly on the lower mass cut-off scale of the substructure mass function. While the amplitude of the expected flux from each dSph depends sensitively on the dark matter model, we show that the flux ratios between the six Sphs are known to within a factor of about 10. The flux ratios are also relatively insensitive to the current theoretical range of cold dark matter halo central slopes and substructure fractions.

Figures (5)

• Figure 1: The velocity dispersion profiles for Ursa Minor, with data from Palma:2002mw. The short-dashed curve shows a model with $\rho_s = 10^8 \, {\rm M_\odot} \, {\rm kpc}^{-3}$ and $r_s = 0.63 \, {\rm kpc}$, while the long-dashed curve depicts a model with $\rho_s = 10^7 \, {\rm M_\odot} \, {\rm kpc}^{-3}$ and $r_s = 3.1 \, {\rm kpc}$. Both curves have $\beta = 0.6$.
• Figure 2: The allowed region in the $\rho_s-r_s$ plane for the six dSphs after marginalizing over the stellar velocity dispersion anisotropy parameter $\beta$. Solid lines correspond to contours with $V_{\rm max}$ of 5, 10, 20, 40, 80, 150 ${\rm km}\,{\rm s}^{-1}$. Long-dashed lines represent the $\rho_s-r_s$ relation as derived from the field halo relation, and the 2-$\sigma$ scatter above the median concentration vs. mass relation. Dot-dashed lines represent the $\rho_s-r_s$ relation as derived from the tidally-stripped halo relation, and the 2-$\sigma$ scatter below the median concentration vs. mass relation.
• Figure 3: The allowed region in the $\rho_s^2 r_s^3- \rho_s$ plane for each dSph after marginalizing over the stellar velocity dispersion anisotropy parameter $\beta$ filled region, and contour levels for the expected $\gamma$-ray flux. Contours are shown for $\log_{10}[dN_\gamma / dAdt]=-13$, $-12$, $-11$, & $-10$, where the flux is measured in photons ${\rm cm}^{-2}{\rm s}^{-1}$. Solid contours depict the flux expected within a region of radius 2 degrees centered on the dwarf, while dot-dashed contours depict the same flux thresholds for a region of radius 0.1 degree centered on the dwarf. The hatched regions represent the preferred region from CDM theoretical modeling (see Fig. \ref{['fig:vmaxfigure']} and discussion in text).
• Figure 4: Examples of the flux spectrum of Ursa Minor for three cases where the quanitities $(\log_{10}\rho_s,\log_{10}r_s,M_\chi)$ take the values of (7.4,0.033,46) depicted with the long-dashed line, (7.9,-0.067,46) shown as a short-dashed line, and (7.9,-0.067,500) shown as the dot-dashed line. The value of ${\cal L}$ that corresponds to these 3 cases is $[2.08\times 10^{14}, 1.25 \times 10^{15}, 1.25 \times 10^{15}] {\rm GeV} \, {\rm cm}^{-2} {\rm s}^{-1}$ respectively. The units for $\rho_s$ are ${\rm M_\odot} \, {\rm kpc}^{-3}$, while $r_s$ is in kpc and $M_\chi$ in GeV. No enhancement of flux from substructure is included; substructure could increase the flux by up to a factor of 100, increasing the prospects for detection. The calculated flux is integrated over an angular region of radius 0.1 degrees centered on the dSph, and the value of ${\cal P } = {\cal P } _{\rm SUSY} \approx 10^{-28} {\rm cm}^3 {\rm s}^{-1} {\rm GeV}^{-2}$, which corresponds to the most optimistic scenario for supersymmetric dark matter (see Sec. \ref{['section:CDMhalos']}). Open squares show the amplitude of the $\gamma-$ray extragalactic emission Sreekumar:1997un, while filled circles correspond to the galactic emission of $\gamma$-rays at high galactic latitudes HETAL97.
• Figure 5: Left: The predicted substructure boost factors assuming a subhalo mass function scaling as $dN/dM \sim M^{-1.9}$. Right: The dependence of the overall substructure boost factor to the slope of the subhalo mass function for Ursa Minor. The assumed parameters are $M = 3.02 \times 10^8 {\rm M_\odot}$, $\rho_s = 6.3 \times 10^7 {\rm M_\odot} \, {\rm kpc}^{-3}$, and $r_s = 0.8 \, {\rm kpc}$.